Trapezoidal Profile Time
Compute the total time of a motion with a trapezoidal velocity profile, t = d/Vmax + Vmax/a, adding the cruise-velocity time to the acceleration and deceleration phases. It is the most common motion profile in motors and robots: accelerate to maximum speed, hold constant and decelerate. Enter the distance, the maximum velocity and the acceleration (assuming equal acceleration and deceleration).
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Tempo de perfil trapezoidal
O perfil trapezoidal de velocidade é a forma mais comum de comandar um movimento em motores e robôs: acelera a partir do repouso a uma taxa constante até atingir a velocidade máxima, cruza nessa velocidade, e desacelera simetricamente até parar. O gráfico velocidade × tempo forma um trapézio. O tempo total é t = d/Vmáx + Vmáx/a: o primeiro termo seria o tempo se a velocidade fosse máxima o tempo todo, e o segundo acrescenta o atraso das rampas de aceleração e desaceleração. (A fórmula vale quando há distância suficiente para atingir Vmáx; em movimentos curtos, o perfil vira um triângulo e não chega à velocidade máxima.) Informe a distância, a velocidade máxima e a aceleração.
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Jerk (Rate of Acceleration Change)
Compute the jerk, J = Δacceleration/Δtime, the rate of change of acceleration over time — the third derivative of position. High jerk causes jolts, vibration and wear; controlling it (jerk-limited or S-curve profiles) makes motion smooth, protecting mechanisms and improving the finish on CNC machines and elevators. Enter the acceleration change and the time interval.
Servo Torque for Arm
Calculate the static torque a servomotor needs to hold a horizontal arm, T = m·g·L, from the tip mass m, gravity g (9.81 m/s²) and the arm length L. The result, in N·m, is the minimum torque the servo must provide to keep the arm horizontal against the load weight — the most unfavorable position. It is essential in designing robotic arms, grippers and servo-driven mechanisms, sizing the motor with a safety margin over this value. For arms with their own mass, the center of mass is used. Enter the mass and the arm length.
Follower Displacement (Parabolic)
Calculate the displacement of a parabolic-motion cam follower, in the first half of the rise, s = 2·h·(θ/β)², from the total lift h (mm), the cam angle θ (rad, current position) and the rise angle β (rad). In parabolic (constant-acceleration) motion, the first HALF of the rise has the follower accelerating uniformly, and its displacement grows with the SQUARE of the angle — hence 'parabolic' (the s vs θ curve is a parabola). The formula s = 2h(θ/β)² holds for θ between 0 and β/2 (half the rise); in the second half, the follower decelerates and the curve is an inverted parabola completing the lift smoothly to h. This motion is the cam analog of a body in free fall (constant acceleration): just as distance traveled grows with the square of time, here displacement grows with the square of angle. The parabolic construction produces the lowest maximum acceleration among simple laws, but with infinite jerk at the junctions (start, middle and end), limiting its use at high speed. This calculation gives the follower position at any point of the first half, useful for tracing the cam profile and for kinematic analysis. Enter the lift, the current angle and the rise angle.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.